Asynchronous l1 positive filter design for switched positive systems with overlapped detection delay

In this study, the asynchronous l positive filtering problem for a class of switched positive system with detection delay is investigated. The switched sequence satisfies modal-dwell-time (MDT) condition and the detection delay is both time-varying and allowed to be overlapped with each other. A new linear copositive Lyapunov function, which is time-dependent, mode-dependent and MDT-dependent, is constructed and the stability of the underlying filtering error system is established. Based on the established stability result, conditions guaranteeing the l stability of the corresponding filtering error system are further derived. The allowable total running time of the unmatched sub-filters is presented to be upper bounded by a linear combination of those running on matched sub-filters. An asynchronous positive filter with l disturbance suppression performance for the underlying switched positive system with overlapped detection delay is designed by solving a linear programming problem. The effectiveness of the proposed filter is illustrated by a numerical example.